Final answer:
The rhetorical device used in the phrase is a metaphor, which compares the fossil-fuel industry's tactics to a 'dirty game' directly, without using 'like' or 'as'.
Step-by-step explanation:
The phrase 'The fossil-fuel industry’s dirty game of corporate politics was on display...' uses a rhetorical device known as a metaphor. By directly comparing the industry's tactics to a 'dirty game,' it implies that the actions are underhanded or dishonest without using the words 'like' or 'as', which distinguishes a metaphor from a simile.